51 research outputs found
Fractal and multifractal descriptors restore ergodicity broken by non-Gaussianity in time series
Ergodicity breaking is a challenge for biological and psychological sciences.
Ergodicity is a necessary condition for linear causal modeling. Long-range
correlations and non-Gaussianity characterizing various biological and
psychological measurements break ergodicity routinely, threatening our capacity
for causal modeling. Long-range correlations (e.g., in fractional Gaussian
noise, a.k.a. "pink noise") break ergodicity--in raw Gaussian series, as well
as in some but not all standard descriptors of variability, i.e., in
coefficient of variation (CV) and root mean square (RMS) but not standard
deviation (SD) for longer series. The present work demonstrates that
progressive increases in non-Gaussianity conspire with long-range correlations
to break ergodicity in SD for all series lengths. Meanwhile, explicitly
encoding the cascade dynamics that can generate temporally correlated
non-Gaussian noise offers a way to restore ergodicity to our causal models.
Specifically, fractal and multifractal properties encode both scale-invariant
power-law correlations and their variety, respectively, both of which features
index the underlying cascade parameters. Fractal and multifractal descriptors
of long-range correlated non-Gaussian processes show no ergodicity breaking and
hence, provide a more stable explanation for the long-range correlated
non-Gaussian form of biological and psychological processes. Fractal and
multifractal descriptors offer a path to restoring ergodicity to causal
modeling in these fields.Comment: 33 pages, 11 figures. arXiv admin note: text overlap with
arXiv:2202.0109
Multifractality, Interactivity, and the Adaptive Capacity of the Human Movement System: A Perspective for Advancing the Conceptual Basis of Neurologic Physical Therapy
Background and Purpose:
Physical therapists seek to optimize movement as a means of reducing disability and improving health. The short-term effects of interventions designed to optimize movement ultimately are intended to be adapted for use across various future patterns of behavior, in potentially unpredictable ways, with varying frequency, and in the context of multiple tasks and environmental conditions. In this perspective article, we review and discuss the implications of recent evidence that optimal movement variability, which previously had been associated with adaptable motor behavior, contains a specific complex nonlinear feature known as “multifractality.” Summary of Key Points:
Multifractal movement fluctuation patterns reflect robust physiologic interactivity occurring within the movement system across multiple time scales. Such patterns provide conceptual support for the idea that patterns of motor behavior occurring in the moment are inextricably linked in complex, physiologic ways to patterns of motor behavior occurring over much longer periods. The human movement system appears to be particularly tuned to multifractal fluctuation patterns and exhibits the ability to reorganize its output in response to external stimulation embedded with multifractal features. Recommendations for Clinical Practice:
As a fundamental feature of human movement, multifractality opens new avenues for conceptualizing the link between physiologic interactivity and adaptive capacity. Preliminary evidence supporting the positive influence of multifractal rhythmic auditory stimulation on the gait patterns of individuals with Parkinson disease is used to illustrate how physical therapy interventions might be devised to specifically target the adaptive capacity of the human movement system.
Video Abstract available for more insights from the authors (see Video, Supplemental Digital Content 1, https://links.lww.com/JNPT/A183)
The relationship between foot arch measurements and walking parameters in children
BACKGROUND: Walking mechanics are influenced by body morphology. Foot arch height is one aspect of body morphology central to walking. However, generalizations about the relationship between arch height and walking are limited due to previous methodologies used for measuring the arch and the populations that have been studied. To gain the knowledge needed to support healthy gait in children and adults, we need to understand this relationship in unimpaired, typically developing children and adults using dynamic measures. The purpose of the current study was to examine the relationship between arch height and gait in a sample of healthy children and adults using dynamic measures. METHODS: Data were collected from 638 participants (n = 254 children and n = 384 adults) at the Museum of Science, Boston (MOS) and from 18 4- to 8-year-olds at the Motor Development and Motor Control Laboratories. Digital footprints were used to calculate two arch indices: the Chippaux-Smirak (CSI) and the Keimig Indices (KI). The height of the navicular bone was measured. Gait parameters were captured with a mechanized gait carpet at the MOS and three-dimensional motion analyses and in-ground force plates in the Motor Development and Motor Control Laboratories. RESULTS: Linear regression analyses on data from the MOS confirmed that as age increases, step length increases. With a linear mixed effect regression model, we found that individuals who took longer steps had higher arches as measured by the KI. However, this relationship was no longer significant when only adults were included in the model. A model restricted to children found that amongst this sample, those with higher CSI and higher KI values take longer relative step lengths. Data from the Motor Development and Motor Control Laboratories showed that both CSI and KI added to the prediction; children with lower anterior ground reaction forces had higher CSI and higher KI values. Arch height indices were correlated with navicular height. CONCLUSIONS: These results suggest that more than one measure of the arch may be needed elucidate the relationship between arch height and gait.K12 HD055931 - NICHD NIH HHS; K12HD055931 - NICHD NIH HH
Bringing the Nonlinearity of the Movement System to Gestural Theories of Language Use: Multifractal Structure of Spoken English Supports the Compensation for Coarticulation in Human Speech Perception
Coarticulation is the tendency for speech vocalization and articulation even at the phonemic level to change with context, and compensation for coarticulation (CfC) reflects the striking human ability to perceive phonemic stability despite this variability. A current controversy centers on whether CfC depends on contrast between formants of a speech-signal spectrogram—specifically, contrast between offset formants concluding context stimuli and onset formants opening the target sound—or on speech-sound variability specific to the coordinative movement of speech articulators (e.g., vocal folds, postural muscles, lips, tongues). This manuscript aims to encode that coordinative-movement context in terms of speech-signal multifractal structure and to determine whether speech's multifractal structure might explain the crucial gestural support for any proposed spectral contrast. We asked human participants to categorize individual target stimuli drawn from an 11-step [ga]-to-[da] continuum as either phonemes “GA” or “DA.” Three groups each heard a specific-type context stimulus preceding target stimuli: either real-speech [al] or [a], sine-wave tones at the third-formant offset frequency of either [al] or [aɹ], and either simulated-speech contexts [al] or [aɹ]. Here, simulating speech contexts involved randomizing the sequence of relatively homogeneous pitch periods within vowel-sound [a] of each [al] and [aɹ]. Crucially, simulated-speech contexts had the same offset and extremely similar vowel formants as and, to additional naïve participants, sounded identical to real-speech contexts. However, randomization distorted original speech-context multifractality, and effects of spectral contrast following speech only appeared after regression modeling of trial-by-trial “GA” judgments controlled for context-stimulus multifractality. Furthermore, simulated-speech contexts elicited faster responses (like tone contexts do) and weakened known biases in CfC, suggesting that spectral contrast depends on the nonlinear interactions across multiple scales that articulatory gestures express through the speech signal. Traditional mouse-tracking behaviors measured as participants moved their computer-mouse cursor to register their “GA”-or-“DA” decisions with mouse-clicks suggest that listening to speech leads the movement system to resonate with the multifractality of context stimuli. We interpret these results as shedding light on a new multifractal terrain upon which to found a better understanding in which movement systems play an important role in shaping how speech perception makes use of acoustic information
Fractality of Body Movements Predicts Perception of Affordances: Evidence From Stand-On-Ability Judgments About Slopes
We recorded head motion with one wireless marker attached to the back of the head during quiet stance as participants visually inspected a sloped ramp in order to perceive whether they might be able to stand on the surface. Participants responded with yes or no without attempting to stand on the ramp. As has been found in dynamic touch (Palatinus, Kelty-Stephen, Kinsella-Shaw, Carello, & Turvey, 2014), we hypothesized that multiscale fluctuation patterns in bodily movement during visual observation would predict perceptual judgments. Mixed-effects logistic regression predicted binary affordance judgments as a function of geographical slant angle, head-motion standar deviation, and multifractal spectrum width (Ihlen, 2012). Multifractal spectrum width was the strongest predictor of affordance judgments. Specifically, increased spectrum width predicted decreased odds of a yes answer. Interestingly, standard deviation was not a significant predictor, reinforcing our prediction that traditional measures of variability fail to account for what fractal measures of multiscale interactions can predict about information pickup in perception-action systems
The relationship between foot arch measurements and walking parameters in children
Background: Walking mechanics are influenced by body morphology. Foot arch height is one aspect of body morphology central to walking. However, generalizations about the relationship between arch height and walking are limited due to previous methodologies used for measuring the arch and the populations that have been studied. To gain the knowledge needed to support healthy gait in children and adults, we need to understand this relationship in unimpaired, typically developing children and adults using dynamic measures. The purpose of the current study was to examine the relationship between arch height and gait in a sample of healthy children and adults using dynamic measures.
Methods: Data were collected from 638 participants (n = 254 children and n = 384 adults) at the Museum of Science, Boston (MOS) and from 18 4- to 8-year-olds at the Motor Development and Motor Control Laboratories. Digital footprints were used to calculate two arch indices: the Chippaux-Smirak (CSI) and the Keimig Indices (KI). The height of the navicular bone was measured. Gait parameters were captured with a mechanized gait carpet at the MOS and three-dimensional motion analyses and in-ground force plates in the Motor Development and Motor Control Laboratories.
Results: Linear regression analyses on data from the MOS confirmed that as age increases, step length increases. With a linear mixed effect regression model, we found that individuals who took longer steps had higher arches as measured by the KI. However, this relationship was no longer significant when only adults were included in the model. A model restricted to children found that amongst this sample, those with higher CSI and higher KI values take longer relative step lengths. Data from the Motor Development and Motor Control Laboratories showed that both CSI and KI added to the prediction; children with lower anterior ground reaction forces had higher CSI and higher KI values. Arch height indices were correlated with navicular height.
Conclusions: These results suggest that more than one measure of the arch may be needed elucidate the relationship between arch height and gait
The relationship between foot arch measurements and walking parameters in children
Walking mechanics are influenced by body morphology. Foot arch height is one aspect of body morphology central to walking. However, generalizations about the relationship between arch height and walking are limited due to previous methodologies used for measuring the arch and the populations that have been studied. To gain the knowledge needed to support healthy gait in children and adults, we need to understand this relationship in unimpaired, typically developing children and adults using dynamic measures. The purpose of the current study was to examine the relationship between arch height and gait in a sample of healthy children and adults using dynamic measures
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